We have,
Mean (service time) = 01:06 minutes per customer (read clock as min:sec)
SD (service time) = 00:06 min
Mean (arrival time) = 00:37 min per customer
SD (arrival time) = 00:06 min
And n = 41 customers
95% Confidence Intervals for Service Time:
Mean(service time) - 1.96 (SE(service time)) = 54 sec/customer
Mean(service time) + 1.96 (SE(service time)) = 78 sec/customer
SE = SD/sqrt(n)
95% Confidence Intervals for Service Rate:
1/[Mean(service time) + 1.96 (SE(service time))] = 0.01282 = 46 customers/sec
1/[Mean(service time) - 1.96 (SE(service time))] = 0.01852 = 67 customers/sec**
** (0.01852 sec *60 *60)
95% Confidence Intervals for Arrival Time:
Mean(arrival time) – 1.96 (SE(arrival time)) = 24 sec /customer
Mean(arrival time) + 1.96 (SE(arrival time)) = 49 sec /customer
95% Confidence Intervals for Arrival Rate:
1/[Mean(arrival time) + 1.96 (SE(arrival time))] = 0.02041 = 73 customers/sec**
1/[Mean(arrival time) - 1.96 (SE(arrival time))] = 0.04167 = 150 customers/sec
** (0.02041 sec *60 *60)